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Mathematics in Computer Science

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01-03-2022

Non-homogeneous Chain of Harmonic Oscillators

Authors: Luís Bandeira, Carlos Correia Ramos

Published in: Mathematics in Computer Science | Issue 1/2022

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Abstract

We study vibrational properties of non-homogeneous materials. These are idealized materials composed by one dimensional chains of harmonic oscillators represented by an alternating sequence of particles and springs. Although the system is linear, thus possesses exact explicit solutions, the formulas for the solutions can be complicated. Homogeneous chains are used as basic building blocks for the characterization of the system global dynamics. In particular, we determine the solutions for a system composed of two distinct homogeneous chains in terms of the original solutions for these two homogeneous chains, when uncoupled. We explore different kinds of possible couplings, each with a distinct physical meaning.

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Title: Non-homogeneous Chain of Harmonic Oscillators
Authors: Luís Bandeira
Carlos Correia Ramos
Publication date: 01-03-2022
Publisher: Springer International Publishing
Published in: Mathematics in Computer Science / Issue 1/2022
Print ISSN: 1661-8270
Electronic ISSN: 1661-8289
DOI: https://doi.org/10.1007/s11786-022-00522-x

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